Question: Solve for $x$ : $x^2 - 17x + 70 = 0$
Answer: The coefficient on the $x$ term is $-17$ and the constant term is $70$ , so we need to find two numbers that add up to $-17$ and multiply to $70$ The two numbers $-10$ and $-7$ satisfy both conditions: $ {-10} + {-7} = {-17} $ $ {-10} \times {-7} = {70} $ $(x {-10}) (x {-7}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -10) (x -7) = 0$ $x - 10 = 0$ or $x - 7 = 0$ Thus, $x = 10$ and $x = 7$ are the solutions.